Chapter 13: Statistics Quiz
They may seem boring when you’re younger, but statistics are absolutely fascinating when you get down to the nitty-gritty of them. Today we’ll be doing just that by testing your knowledge on statistics, what kinds of data it deals with and what it’s used for. Good luck!
Questions and Answers
- 1.
The art and science of gathering, analyzing, and making inferences (predictions) from numerical information obtained in an experiment
- A.
Population
- B.
Statistics
- C.
cluster sample
- D.
Class mark
Correct Answer
B. StatisticsExplanation
Statistics is the correct answer because it refers to the art and science of gathering, analyzing, and making inferences or predictions from numerical information obtained in an experiment. It involves the collection, organization, interpretation, presentation, and analysis of data to understand patterns, trends, and relationships. Statistics provide a way to summarize and describe data, make informed decisions, and draw conclusions about a population based on a sample.Rate this question:
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- 2.
As the numerical information so obtained is referred
- A.
unbiased sample
- B.
area sample
- C.
frequency distribution
- D.
Data
Correct Answer
D. Data -
- 3.
Is concerned with the collection, organization, and analysis of data
- A.
Descriptive statistics
- B.
Inferential statistics
- C.
random number generator
- D.
piece of data
Correct Answer
A. Descriptive statisticsExplanation
Descriptive statistics involves the collection, organization, and analysis of data. It focuses on summarizing and describing the main features of a dataset, such as central tendency (mean, median, mode) and dispersion (range, variance, standard deviation). This branch of statistics is used to present and interpret data in a meaningful way, providing insights into patterns, trends, and characteristics of the data. It does not involve making inferences or drawing conclusions about a larger population, which is the domain of inferential statistics.Rate this question:
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- 4.
Is concerned with making generalizations or predictions from the data collected
- A.
Descriptive statistics
- B.
Inferential statistics
- C.
random number generator
- D.
Piece of data
Correct Answer
B. Inferential statisticsExplanation
Inferential statistics is the correct answer because it involves making generalizations or predictions from the data collected. Descriptive statistics, on the other hand, is concerned with summarizing and describing the data without making any inferences or predictions. A random number generator is a tool used to generate random numbers, which is unrelated to making generalizations or predictions from data. A piece of data is a singular unit of information and does not pertain to the process of making generalizations or predictions.Rate this question:
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- 5.
The entire contents of the box constitute the population, it consists of all items or people of interest
- A.
Population
- B.
area sample
- C.
Frequency distribution
- D.
midpoint of a class
Correct Answer
A. PopulationExplanation
The correct answer is "Population" because it refers to the entire contents of the box, which includes all the items or people of interest. In statistics, a population is the complete set of individuals, items, or data that is being studied or analyzed. It is important to define the population accurately in order to draw valid conclusions and make generalizations about the entire group.Rate this question:
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- 6.
It’s the statistician often uses a subset of the population
- A.
Statistics
- B.
random number table
- C.
Sample
- D.
convenience sample
Correct Answer
C. SampleExplanation
A sample is a subset of the population that is selected for statistical analysis. It is a common practice for statisticians to use a sample instead of studying the entire population, as it is often more practical and cost-effective. By analyzing a representative sample, statisticians can make inferences and draw conclusions about the larger population. Therefore, the use of a sample is a common and important tool in statistical analysis.Rate this question:
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- 7.
The sum of the data divided by the number of pieces of data,it is used when the mean of a sample of the population is calculated
- A.
s
- B.
µ
- C.
¯x (x bar)
- D.
σ
Correct Answer
C. ¯x (x bar)Explanation
The symbol ¯x (x bar) represents the mean of a sample of data. The mean is calculated by summing up all the data points and dividing it by the number of data points. It is a measure of central tendency that provides an average value for the data set. The mean is commonly used in statistics to analyze and compare different sets of data.Rate this question:
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- 8.
Standard deviation, measures how much the data differ from the mean. It is used when the standard deviation by of a sample is calculated
- A.
σ
- B.
S
- C.
µ
- D.
¯x (x bar)
Correct Answer
B. SExplanation
The correct answer is "s". Standard deviation is a measure of how much the data points in a sample differ from the mean. It is commonly denoted by the symbol "s" when calculating the standard deviation of a sample.Rate this question:
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- 9.
The sum of the data divided by the number of pieces of data, it is used when the mean of a sample of the entire population is calculated
- A.
¯x (x bar)
- B.
µ
- C.
σ
- D.
S
Correct Answer
B. µExplanation
The symbol µ represents the mean of a sample of the entire population. The mean is calculated by summing up all the data and dividing it by the number of pieces of data. This is a commonly used statistical measure to determine the average value of a dataset.Rate this question:
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- 10.
Standard deviation, measures how much the data differ from the mean, it is used when the standard deviation of the entire population is calculated
- A.
¯x (x bar)
- B.
µ
- C.
σ
- D.
S
Correct Answer
C. σExplanation
Standard deviation (σ) is the correct answer because it is a statistical measure that quantifies the amount of variation or dispersion in a set of data. It indicates how much the data points deviate from the mean. Standard deviation is used when calculating the standard deviation of the entire population, as opposed to a sample. It provides valuable information about the spread of the data and helps in understanding the distribution of the population.Rate this question:
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- 11.
Is one that is a religion, political affiliation, age, and so on…
- A.
Systematic sample
- B.
Frequency distribution
- C.
convenience sample
- D.
Unbiased sample
Correct Answer
D. Unbiased sampleExplanation
An unbiased sample refers to a subset of a population that is selected without any bias or preference towards certain characteristics or traits. It ensures that every individual in the population has an equal chance of being included in the sample, which helps to eliminate any potential sources of bias and provides a more accurate representation of the entire population.Rate this question:
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- 12.
If a sample is drawn in such a way that each time an item is selected each item in the population has an equal chance of being drawn.
- A.
random sample
- B.
Cluster sample
- C.
systematic sample
- D.
convenience sample
Correct Answer
A. random sampleExplanation
A random sample is the correct answer because it is drawn in a way that ensures each item in the population has an equal chance of being selected. This means that the selection process is unbiased and representative of the entire population. Other sampling methods like cluster sampling, systematic sampling, and convenience sampling may introduce biases and may not provide an accurate representation of the population.Rate this question:
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- 13.
When a sample is obtained by drawing every nth item on a list or production line.
- A.
convenience sample
- B.
Random sample
- C.
systematic sample
- D.
cluster sample
Correct Answer
C. systematic sampleExplanation
A systematic sample is obtained by selecting every nth item on a list or production line. This method ensures that the sample is representative of the entire population and reduces the potential for bias. By following a systematic approach, every item has an equal chance of being selected, providing a fair representation of the population. This sampling technique is commonly used in research and statistical analysis to gather data efficiently and accurately.Rate this question:
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- 14.
Is sometimes referred to as an area sample because it is frequently applied on a geographical basis
- A.
convenience sample
- B.
Random sample
- C.
systematic sample
- D.
cluster sample
Correct Answer
D. cluster sampleExplanation
A cluster sample is sometimes referred to as an area sample because it is frequently applied on a geographical basis. In a cluster sample, the population is divided into clusters or groups based on their geographical location. Then, a random selection of clusters is chosen, and all individuals within the selected clusters are included in the sample. This method is often used when it is impractical or costly to sample individuals from the entire population, making it convenient to select clusters instead.Rate this question:
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- 15.
It uses data that are easily or readily obtained
- A.
convenience sample
- B.
Random sample
- C.
systematic sample
- D.
cluster sample
Correct Answer
A. convenience sampleExplanation
A convenience sample is a type of sampling method where the researcher selects individuals who are easily accessible or readily available to participate in the study. This means that the data collected from a convenience sample is based on the individuals who are convenient to include in the study, rather than being randomly selected or systematically chosen. Therefore, the explanation for the given correct answer is that a convenience sample uses data that are easily or readily obtained.Rate this question:
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- 16.
It is a device, usually a calculator or computer program, that produces a list of random number
- A.
random number table
- B.
Random number generator
- C.
area sample
Correct Answer
B. Random number generatorExplanation
A random number generator is a device or program that generates a list of random numbers. It is commonly used in various applications such as simulations, cryptography, and statistical sampling. Unlike a random number table, which is a pre-determined list of random numbers, a random number generator produces random numbers on the fly. It uses algorithms and seed values to generate pseudo-random numbers that appear to be random but are actually determined by a set of rules. This makes it a versatile tool for generating random values in a wide range of scenarios.Rate this question:
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- 17.
It is a collection of random digits in which each digits has an equal chance or appearing
- A.
random number table
- B.
Random number generator
- C.
area sample
Correct Answer
A. random number tableExplanation
A random number table is a collection of random digits that are generated in a way that each digit has an equal chance of appearing. This means that there is no pattern or bias in the selection of the digits. It is commonly used in statistical sampling and simulations to generate random numbers for various purposes.Rate this question:
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- 18.
When a population is divided into parts, called strata, for the purpose of drawing a sample
- A.
unbiased sample
- B.
piece of data
- C.
stratified sampling
- D.
class width
Correct Answer
C. stratified samplingExplanation
Stratified sampling is the correct answer because it refers to the process of dividing a population into distinct subgroups or strata based on certain characteristics. This method is used to ensure that the sample drawn from each stratum is representative of the entire population. By stratifying the population, researchers can obtain a more accurate and unbiased sample, as it allows for proportional representation of different groups within the population. This technique is commonly used in surveys and research studies to improve the reliability and validity of the findings.Rate this question:
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- 19.
Known as class, when a population has varied characteristics and then take a random sample from each of class.
- A.
stratum
- B.
Piece of data
- C.
Descriptive statistics
- D.
Population
Correct Answer
A. stratumExplanation
In statistics, a population refers to the entire group of individuals or objects that are being studied. When a population has varied characteristics, it can be divided into subgroups or classes known as strata. Each stratum represents a subset of the population with similar characteristics. Taking a random sample from each stratum helps ensure that the sample is representative of the entire population and accounts for the variability within each class. Therefore, the term "stratum" is the correct answer in this context.Rate this question:
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- 20.
It is a single response to an experiment. When the amount of date is large, it is usually advantageous to construct a frequency distribution
- A.
Piece of data
- B.
class width
- C.
class mark
- D.
histogram
Correct Answer
A. Piece of dataExplanation
A "piece of data" refers to a single value or observation collected during an experiment. When there is a large amount of data, constructing a frequency distribution can be beneficial. A frequency distribution organizes the data into classes or intervals, making it easier to understand and analyze. It helps to identify patterns, trends, and the distribution of the data. Therefore, the given answer is correct as it accurately describes the importance of constructing a frequency distribution when dealing with a large amount of data.Rate this question:
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- 21.
A listing of the observed values and the corresponding frequency of occurrence of each value
- A.
stem-and-leaf display
- B.
frequency polygon
- C.
frequency distribution
- D.
measures of central tendency
Correct Answer
C. frequency distributionExplanation
A frequency distribution is a listing of the observed values and the corresponding frequency of occurrence of each value. It presents the data in a tabular format, showing how often each value appears in the data set. This allows for a clear understanding of the distribution and patterns within the data. It is commonly used to summarize and analyze data in statistics and research.Rate this question:
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- 22.
To determine how far, in terms of standard deviations, a given score is from the mean of the distribution
- A.
z-score
- B.
rectangular distribution
- C.
Measures of dispersion
- D.
Measures of position
Correct Answer
A. z-scoreExplanation
The z-score is used to determine how far a given score is from the mean of a distribution in terms of standard deviations. It is a measure of position that allows for comparison and interpretation of scores across different distributions. The z-score is calculated by subtracting the mean from the score and dividing the result by the standard deviation. It provides a standardized value that can be used to assess the relative position of a score within a distribution.Rate this question:
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- 23.
It divided data into 4 equal parts, the 1st is the value that is higher than about ¼ or 25% of the population, the 2nd is the value that is higher than about ½ the population and is the same as the 50th percentile, or the median, the 3rd is the value that is higher than about ¾ of the population and is the same as the 75th percentile
- A.
median
- B.
measures of position
- C.
percentile
- D.
quartiles
Correct Answer
D. quartilesExplanation
The explanation for the correct answer, quartiles, is that quartiles are a measure of position that divide data into four equal parts. The first quartile represents the value that is higher than about 25% of the population, the second quartile represents the median or the value that is higher than about 50% of the population, and the third quartile represents the value that is higher than about 75% of the population. Therefore, quartiles are used to understand the distribution and spread of data by dividing it into equal parts.Rate this question:
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- 24.
The mean, median, and mode all have the same value
- A.
skewed distribution
- B.
Gaussian distribution
- C.
J-shaped distribution
- D.
Rectangular distribution
Correct Answer
B. Gaussian distributionExplanation
A Gaussian distribution, also known as a normal distribution, is a symmetrical probability distribution where the mean, median, and mode all have the same value. In this type of distribution, the data is evenly spread around the mean, resulting in a bell-shaped curve. This indicates that the majority of the data falls close to the mean, with fewer values further away from it. Therefore, a Gaussian distribution is the most likely explanation for the mean, median, and mode having the same value.Rate this question:
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- 25.
It has more of a “tail” on one side than the other
- A.
Gaussian distribution
- B.
skewed distribution
- C.
J-shaped distribution
- D.
Rectangular distribution
Correct Answer
B. skewed distributionExplanation
A skewed distribution is a type of probability distribution where the data is not symmetrically distributed around the mean. In this case, the statement suggests that the distribution has more values on one side than the other, indicating a lack of symmetry. This is a characteristic of a skewed distribution, where the tail on one side is longer or more pronounced than the other. This can occur in both positive and negative directions, resulting in positively or negatively skewed distributions. Therefore, the correct answer is a skewed distribution.Rate this question:
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- 26.
Is one in which two nonadjacent values occur more frequently than any other values in a set of data
- A.
bimodal distribution
- B.
Gaussian distribution
- C.
J-shaped distribution
- D.
rectangular distribution
Correct Answer
A. bimodal distributionExplanation
A bimodal distribution is a type of distribution where there are two distinct peaks or modes in the data. This means that there are two nonadjacent values that occur more frequently than any other values in the set of data. This can occur when there are two different groups or populations within the data, each with their own distinct characteristics or behaviors.Rate this question:
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- 27.
The frequency is either constantly increasing or decreasing
- A.
bimodal distribution
- B.
Gaussian distribution
- C.
J-shaped distribution
- D.
rectangular distribution
Correct Answer
C. J-shaped distributionExplanation
A J-shaped distribution is characterized by a small number of low values and a large number of high values. In this type of distribution, the frequency either constantly increases or decreases, resulting in a shape that resembles the letter J. This distribution is often observed in situations where there is a strong bias towards extreme values, such as in income distribution where there are a few individuals with very high incomes and a large number of individuals with low incomes.Rate this question:
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- 28.
All the observed values occur with the same frequency
- A.
Bimodal distribution
- B.
Gaussian distribution
- C.
J-shaped distribution
- D.
rectangular distribution
Correct Answer
D. rectangular distributionExplanation
A rectangular distribution is characterized by all observed values occurring with the same frequency. In this distribution, there are no outliers or extreme values, and the data is evenly spread across the entire range. This type of distribution is often seen in situations where there is a limited range of possible values and each value is equally likely to occur.Rate this question:
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- 29.
Use to indicate the spread of the data
- A.
bimodal
- B.
Measures of dispersion
- C.
stem-and-leaf display
- D.
Midpoint of a class
Correct Answer
B. Measures of dispersionExplanation
Measures of dispersion are statistical tools used to indicate the spread or variability of data. They provide information about how the data points are distributed around the mean or median. By calculating measures such as range, variance, or standard deviation, we can understand the extent to which the data values deviate from the central tendency. These measures are essential in analyzing and comparing datasets, as they allow us to assess the variability and make meaningful interpretations about the data.Rate this question:
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- 30.
There are 99 percentiles dividing a set of data into 100 equal parts, a score in the nth percentile means that you outperformed about n% of the population who took the test and that (100 – n)% of the people taking the test performed better than you did
- A.
quartiles
- B.
percentile
- C.
bimodal
- D.
average
Correct Answer
B. percentileExplanation
A percentile is a statistical measure used to describe the position of a particular data point within a dataset. In this context, the answer "percentile" is correct because it aligns with the explanation provided. It states that a score in the nth percentile means that you outperformed about n% of the population who took the test, indicating the relative position of the score within the dataset. The explanation also mentions that (100 - n)% of the people taking the test performed better than you did, further emphasizing the concept of percentiles.Rate this question:
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- 31.
Used to make comparisons, such as comparing the scores of individuals from different populations, and are generally used when the amount of data is large
- A.
bimodal
- B.
measures of central tendency
- C.
measures of position
- D.
Frequency distribution
Correct Answer
C. measures of positionExplanation
Measures of position are used to make comparisons between individuals from different populations, especially when dealing with large amounts of data. These measures provide information about the relative position or rank of a particular value within a dataset, such as percentiles or quartiles. By using measures of position, researchers can gain insights into how individuals or groups compare to each other in terms of their scores or values.Rate this question:
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- 32.
If two values in a set of data occur more often than all the other data, we consider both these values as modes
- A.
bimodal
- B.
mode
- C.
Mean
- D.
Median
Correct Answer
A. bimodalExplanation
If two values in a set of data occur more frequently than any other values, we consider both of these values as modes. In other words, if there are two peaks or high points in the data distribution, it is considered bimodal. The term "bimodal" specifically refers to a situation where there are two modes in the data set. The other options, mode, mean, and median, do not specifically address the concept of having two modes in the data.Rate this question:
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- 33.
The pieces of data that occurs most frequently
- A.
Bimodal
- B.
Mode
- C.
Mean
- D.
Median
Correct Answer
B. ModeExplanation
The correct answer is "mode". The mode is the value that appears most frequently in a set of data. It is a measure of central tendency and can be used to describe the most common or typical value in a dataset. In this case, the question is asking for the term that refers to the pieces of data that occur most frequently, which is the mode.Rate this question:
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- 34.
The value in the middle of a set of ranked data
- A.
Bimodal
- B.
Mode
- C.
Median
- D.
Mean
Correct Answer
C. MedianExplanation
The correct answer is median. The median is the value in the middle of a set of ranked data. It is found by arranging the data in ascending order and selecting the middle value. Unlike the mean, which is influenced by extreme values, the median is not affected by outliers. The mode refers to the most frequently occurring value in a dataset, while bimodal means that there are two modes in the dataset.Rate this question:
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- 35.
The total number of pieces of data
- A.
Σ
- B.
Σn
- C.
S
- D.
µ
Correct Answer
B. ΣnExplanation
The given expression Σn represents the sum of all the values of n. In this context, n represents the number of pieces of data. Therefore, the correct answer Σn indicates the total number of pieces of data.Rate this question:
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- 36.
The Greek letter sigma, used to indicated “summation”
- A.
Σ
- B.
Σn
- C.
S
- D.
µ
Correct Answer
A. ΣExplanation
The correct answer is Σ because it is the Greek letter sigma, which is commonly used in mathematics to represent summation. When written above a series of numbers or variables, it indicates that they should be added together.Rate this question:
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- 37.
The sum of the data divided by the number of pieces of data
- A.
Mean
- B.
mode
- C.
Median
- D.
class mark
Correct Answer
A. MeanExplanation
The mean is calculated by finding the sum of all the data values and then dividing it by the total number of data points. It provides a measure of the central tendency of the data set, representing the average value.Rate this question:
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- 38.
Each is calculated differently and may yield different results for the same set of data. Each will result in a number near the center of the data; for this reason, averages are commonly referred to it.
- A.
measures of position
- B.
measures of central tendency
- C.
Measures of dispersion
- D.
piece of data
Correct Answer
B. measures of central tendencyExplanation
Each of the measures of central tendency (mean, median, and mode) calculates a different value that represents the center of the data. These measures may yield different results for the same set of data because they focus on different aspects of the data distribution. However, all of them provide a number that is near the center of the data. This is why they are commonly referred to as measures of central tendency. They help to summarize and understand the overall pattern of the data by providing a single representative value.Rate this question:
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- 39.
A number that is representative of a group of data
- A.
Mode
- B.
Mean
- C.
Average
- D.
modal class
Correct Answer
C. AverageExplanation
The term "average" refers to a number that represents a group of data. It is calculated by adding up all the values in the data set and dividing the sum by the total number of values. The average is often used to provide a general idea of the central tendency of the data and can be influenced by extreme values.Rate this question:
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- 40.
A tool that organizes and groups the data while allowing us to see the actual values that make up the data
- A.
frequency polygon
- B.
circle graph
- C.
midpoint of a class
- D.
stem-and-leaf display
Correct Answer
D. stem-and-leaf displayExplanation
A stem-and-leaf display is a tool that organizes and groups the data while allowing us to see the actual values that make up the data. It provides a visual representation of the data set, where the "stem" represents the leading digits and the "leaves" represent the trailing digits. This display allows for easy identification of the distribution of the data, including the range, gaps, and clusters. It is a useful tool for displaying and analyzing numerical data in a concise and organized manner.Rate this question:
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- 41.
A line graph with scales the same as those of the histogram, that is, the horizontal scale indicates observed values and the vertical scale indicates frequency
- A.
histogram
- B.
Modal class
- C.
frequency polygon
- D.
class mark
Correct Answer
C. frequency polygonExplanation
A frequency polygon is a line graph that represents the frequency distribution of a set of data. In this case, the line graph has the same scales as the histogram, meaning that the horizontal axis represents the observed values and the vertical axis represents the frequency. The frequency polygon connects the midpoints of the histogram bars, creating a line that shows the trend of the data. Therefore, the frequency polygon is the correct answer in this context.Rate this question:
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- 42.
A graph with observed values on its horizontal scale and frequencies on its vertical scale
- A.
histogram
- B.
Circle graph
- C.
Pie chart
- D.
frequency polygon
Correct Answer
A. histogramExplanation
A histogram is a graph that represents the distribution of observed values on its horizontal scale and frequencies on its vertical scale. It is used to display the frequency or count of data within different intervals or bins. Each bar in the histogram represents a specific interval, and the height of the bar indicates the frequency of data falling within that interval. Histograms are commonly used to visualize the distribution of numerical data and to identify patterns or trends in the data.Rate this question:
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- 43.
Also pie chart, used to compare parts of one or more components of the whole to the whole
- A.
histogram
- B.
circle graph
- C.
frequency polygon
- D.
Modal class
Correct Answer
B. circle grapHExplanation
A circle graph, also known as a pie chart, is a visual representation that is used to compare the parts of one or more components of a whole to the whole itself. It is a circular chart divided into sectors, with each sector representing a different category or component. The size of each sector is proportional to the quantity or percentage it represents. Circle graphs are commonly used to display data that can be divided into categories or parts, making it easier to understand the relative proportions and relationships between different components.Rate this question:
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- 44.
Also class mark, is found by adding the lower and upper class limit and dividing the sum by 2
- A.
modal class
- B.
midpoint of a class
- C.
class width
- D.
Class limit
Correct Answer
B. midpoint of a classExplanation
The midpoint of a class refers to the average value of the lower and upper class limits. It is calculated by adding the lower and upper class limits and dividing the sum by 2. This value represents the center of the class interval and is often used as a representative value for the entire class. It helps in summarizing and analyzing data, especially in statistical calculations such as finding the mean, median, and mode of a dataset.Rate this question:
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- 45.
The class with the greatest frequency
- A.
lower class limit
- B.
Modal class
- C.
upper class limit
- D.
class width
Correct Answer
B. Modal classExplanation
The modal class refers to the class in a frequency distribution that has the highest frequency or the most occurrences. It is the class with the greatest frequency, meaning that it contains the most data points or observations. The modal class is often used to identify the most common value or range of values in a dataset.Rate this question:
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- 46.
Any of the data of a group of number would belong to the class given
- A.
Modal class
- B.
class width
- C.
lower class limit
- D.
Upper class limit
Correct Answer
B. class widthExplanation
Class width refers to the range of values that are included in each class interval in a frequency distribution. It determines the size of each interval and helps to organize the data into meaningful groups. In this context, the statement suggests that any data point within a group of numbers would fall within the range defined by the class width.Rate this question:
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